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Phantom Graph of Hyperbola

Phantom Graph of Hyperbola
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2018-07-15 09:25
FunctionCoordinate GeometryComplex NumberGraphing
In collections Phantom Graphs
This example demonstrates the construction and properties of the Phantom Graph of a hyperbola. Key math concepts include complex numbers, coordinate geometry, hyperbola equations, and their graphical transformations. GeoGebra commands and objects used are ComplexRoot, Plane, and CurveCartesian. Suitable for high school and above, helping learners understand the application of complex numbers in coordinate geometry and the symmetry of hyperbolas.

GeoGebra Commands & Parameters

  1. ComplexRoot(1 + x^(2) / A^(2) - c^(2) / B^(2)) → z_1, z_2
  2. Plane((1, c, 1), (0, c, 0), (3, c, 2)) → e
  3. CurveCartesian(0, (B * cos(t)), (A * sin(t)), t, 0, (2 * π)) → h

AI Drawing Prompt Reference

Draw a phantom graph of a hyperbola, incorporating complex numbers and coordinate geometry, to illustrate symmetry through hyperbola equations and graphical transformations, starting with points based on complex roots, then constructing a plane with specific coordinates, and finally plotting a curve derived from the hyperbola's parametric equation to show its shape and symmetry.
The prompt above was compiled from the original drawing commands and is for reference only.